WO1999028839A1 - Method and device for computer assisted determination of an area of oscillation in an electric circuit - Google Patents

Abstract

The electric circuit has an oscillator and other components which are connected to the oscillator. The following steps are carried out in an iterative method whereby the protective circuit parameters of the other components are varied for one entity of said circuit parameters: a circuit stability analysis is carried out for the respective entity and a first value is allocated to said entity in a matrix (100) where all examined entities are stored if the circuit begins to oscillate. If not, a second value is allocated to the entity in the matrix.

Description

description

Method and device for the computer-aided determination of an oscillation range of an electrical circuit

The invention relates to the determination of an oscillation range of an electrical circuit.

In an integrated digital semiconductor circuit, an oscillator is occasionally used to generate the internal work cycle. An oscillator in the context of this document can in particular be a quartz oscillator or also a ceramic oscillator.

The following requirements are placed on an oscillator circuit which has at least one oscillator: 1. The oscillator circuit should oscillate safely within a certain time and the oscillation must not suddenly stop again. 2. The frequency of the oscillator circuit should only change within a predefinable range.

3. The current flowing through the oscillator must not exceed a specifiable value in order to avoid destruction or undesired changes in the behavior of the oscillator.

In order to ensure these requirements, it is known to provide additional components in addition to the oscillator in an oscillator circuit. Possible further components are, for example, electrical resistors, electrical capacitors, electrical inductors, amplifier systems, etc.

The other components cannot always be integrated into the semiconductor circuit. The correct dimensioning of the additional components is a considerable problem. It is therefore necessary to determine on the one hand whether an oscillator circuit can oscillate at all and on the other hand to determine a dimensioning of the other components with which a safe start is guaranteed.

It is known that this problem can only be solved by technical means. For this purpose, an integrated circuit with the oscillator and the necessary additional components is built. The circuit is then checked by measurement technology to determine whether it fulfills the desired behavior with regard to start-up safety, frequency constancy and maximum current load of the oscillator.

In order to determine a favorable dimensioning of the other components, the circuits have to be constructed with the different component values and the measurements have to be checked. In the known method, the component values and the information as to whether the circuit oscillates with the respective dimensions of the further components or not are recorded in a matrix from which the most favorable dimensions for the further components are determined.

This procedure has considerable disadvantages:

1. The known method is time-consuming since the replacement of the components to be varied and the corresponding measurements cannot be automated.

2. The measurement results are inaccurate because manufacturing tolerances cannot be taken into account when manufacturing the integrated circuits or with the oscillator. It is therefore not possible to take the results into account with regard to the different quality of the components.

3. It is only possible with very complex and cost-intensive efforts to produce different operating conditions such as, for example, very high or very low temperature at which the electrical circuit must operate. This leads to a very inaccurate and complex determination of the component values and only to unreliable statements regarding the start-up safety for a given dimensioning of the other components.

A method for analyzing the stability of an electrical circuit is known from [1].

Methods for determining a Hopf bifurcation point are described in [2], [3], [4]. A Hopf bifurcation point is a point on a DC characteristic curve at which there is a change in the examined electrical circuit with regard to its stability behavior, i.e. the point at which the circuit changes from a stable steady state to an oscillating state.

[5] discloses a method for computer-aided iterative determination of the transient response of a quartz oscillator circuit. In this case, a dynamic equilibrium state is alternately determined on a current source substituting the quartz oscillator circuit for a determined, predeterminable operating point and a transient analysis is carried out. The transient analysis is carried out for the circuit with a back-substituted quartz oscillator circuit.

Furthermore, it is known from [6] to determine a periodic description of the state of the technical system based on a high-quality starting solution.

Furthermore, so-called tracking methods from [4] are known with which further periodic solutions for describing the circuit can be determined from a periodic description of the state, in order to thus determine a periodic solution of the circuit at a predefinable operating point. The tracking procedures are also referred to as the predictor-corrector procedure. A method for designing oscillators with minimized noise is known from [8]. In this method, a linear subnetwork, which contains, for example, geometric data of the layout, values of passive electronic components

(Capacitors, inductors, resistors) or parameters of an active element of the oscillator (e.g. parameters of the transistor), calculated in such a way that the phase noise becomes minimal. For this purpose, the signal and noise behavior of the oscillator is described by differential equations. On the condition that the differential equations for the signal behavior are fulfilled, one-sideband phase noise of the oscillator is optimized with direct methods of optimal control.

The invention is based on the problem of specifying, with the aid of computers, an oscillation region of an electrical circuit which has at least one quartz oscillator and further components which are connected to the quartz oscillator, the disadvantages of the prior art described above being avoided.

The problem is solved by the method according to claim 1 and by the device according to claim 6.

In the method, the following steps are carried out iteratively, varying the wiring parameters of the further components, for each instance of the wiring parameters: a stability analysis of the circuit is carried out for the respective instance,

- If the instance is determined to be oscillating, a first value is assigned to the instance in a matrix, the first value indicating that the instance of the circuit is oscillating. All are examined in the matrix

Instances saved. If it is determined for the instance of the circuit that the instance does not oscillate, the in- punch assigned a second value in the matrix, the second value indicating that the instance does not start,

- The start-up range results from the instances to which the first value in the matrix has been assigned.

The device has a processor unit which is set up in such a way that the following steps are carried out iteratively, varying the wiring parameters of the further components, for each instance of the wiring parameters. A stability analysis of the circuit is carried out for the respective instance. If it is determined for the instance of the circuit that the instance of the circuit is oscillating, a first value is assigned to the instance in a matrix, the first value indicating that the instance is oscillating. All examined instances are stored in the matrix. If it is determined for the instance of the circuit that it does not oscillate, a second value is assigned to the instance in the matrix, the second value indicating that the instance of the circuit does not oscillate. The start-up range results from the instances to which the first value in the matrix has been assigned.

An instance is to be understood as the oscillator circuit with certain dimensions of the further components and / or certain temperature conditions, operating conditions and / or certain tolerances of the further components.

The invention provides for the first time a very simple, automated determination of an oscillation range for an oscillator circuit. It is also possible with the invention to take into account components of different quality with different tolerance values. Extreme operating conditions can also be taken into account in the circuit simulation according to the invention. Advantageous developments of the invention result from the dependent claims.

The oscillator can be a quartz oscillator or a ceramic oscillator.

The other components can be electrical resistors, capacitors, inductors, amplifier components, etc.

The stability analysis of the electrical circuit can be carried out using different methods. It has proven to be advantageous to carry out the stability analysis by determining a Hopf bifurcation point for the respective instance. This is an extremely simple and therefore computing time-saving way of stability analysis.

Other options for stability analysis are (during a DC transfer analysis simultaneously):

• a pole zero analysis, • an AC analysis (small signal analysis) using the Bode criterion or the Nyquist criterion,

• a transient analysis.

For some of the instances, the vibration state or dynamic equilibrium of the instance can be calculated at a predefinable operating point using one of the methods described in [2], [3], [4]. This further development also examines for the instance whether the circuit continues to oscillate at the specified operating point. This ensures that the circuit can continue to oscillate safely for the respective instance.

In a further embodiment of the invention, provision is made for the respective transient behavior to be determined for at least some of the instances. This has the advantage that after the transient response has been determined, all the interesting information for the Instance with the respective dimensioning are known. All the desired information about the circuit is available.

An embodiment of the invention is shown in the figures and is explained in more detail below.

Show it

FIG. 1 shows a 2-dimensional matrix in which the start-up range of an electrical circuit is shown for different dimensions of two capacitors; FIG. 2 shows a sketch of an electrical circuit for which the matrix in FIG. 1 was determined; Figure 3 is a bifurcation diagram of an oscillator circuit.

In Fig. 2, an oscillator Q is shown, which is connected to a first terminal 201 on the one hand with a supply voltage VQ and on the other hand with a first capacitance Cχι. The first capacitance Cχι is also connected to ground and to a second capacitance Cχ2. The second capacitance Cχ2 is connected via a second connection 202 to the oscillator Q and an electrical resistor Rχ2. The second resistor Rχ2 is connected via a third connection 203 to an output of an inverter 204 and a ballast resistance bias, both of which in turn are connected to the supply voltage via the first connection 201.

The oscillation range with the associated dimensions (instances) of the further components (first capacitance Cχ, second capacitance C 2 and electrical resistance χ2) is to be determined for the oscillator circuit 200.

To determine the oscillation range of the oscillator circuit 200, the following iterative method is carried out for different instances of the oscillator circuit 200. In each iteration step, an instance, ie a dimensioning or a definition of the further components and the framework conditions (operating conditions, tolerances of the components) is specified.

In this exemplary embodiment, the method is shown on the basis of a predetermined electrical resistance R 2 and predetermined boundary conditions, i.e. the first capacitance C] _ and the second capacitance Cχ2 are each varied in a predeterminable dimensioning interval, which is in each case in a column of a table shown in FIG. 1 for the second capacitance Cχ2 in picofarads (pF) and in one first line for the first capacitance C ι is shown in pF. A stability analysis of the oscillator circuit 200 is carried out for each instance.

This is done by determining the Hopf bifurcation point 301 (cf. FIG. 3). A Hopf bifurcation point 301 is a point of an electrical circuit at which the electrical circuits see from a stable to an unstable, i.e. vibrating state passes.

The Hopf bifurcation point 301 is determined in accordance with one of the methods described in [2], [3], or [4].

Furthermore, it is checked for a specifiable operating point in accordance with the method described below whether the electrical circuit also oscillates stably in the operating point of the circuit.

The Hopf bifurcation point HP is described by a triple, which has an eigenvalue μg, the imaginary part of which is also referred to as the natural frequency of the circuit, a rest position yg of the Hopf bifurcation point HP and an eigenvector V _Q. The Hopf bifurcation point HP is given, for example, by the following triple:

HP = (μo, yo o): = (μ ⁽ λo), y (λo), v (λo)) (1).

The λo is the system parameter λ for which the Hopf bifurcation point HP is obtained for the circuit.

Determination of the bifurcation planes πχ for the respective system parameter λ 102

Starting from the Hopf bifurcation point HP, bifurcation planes πχ are determined in a further step.

For this purpose, the eigenvalue μ (λ) and the eigenvector v (λ) are determined for the system parameter λ and the corresponding solution y (λ) in an environment of the Hopf bifurcation point HP using the corresponding system parameter λo. The Hopf bifurcation point HP results for the special system parameter λo.

One way of forming the bifurcation planes πχ is to use the eigenvectors v (λ) to move through the real parts Re {v (λ)} or the imaginary parts Im {v (λ)} in the complex space C. Eigenvectors v (λ) span the bifurcation planes πχ.

A bifurcation level πχ results according to the following rule:

πχ = {z | z = c • v (λ), c e c} (2).

The IT bifurcation level group is based on the following rule:

Π = {πχ | λ e 9t}. A factor c is any complex number. When using real numbers 9ϊ, the bifurcation plane πχ is two-dimensional, when using complex numbers C, the bifurcation plane πχ is one-dimensional.

By using the bifurcation level πχ and thus a transformation of the entire possible state space, in a complex technical system, which is described by a higher number of differential algebraic equations, from a very high-dimensional state space to determine the periodic state description to a lower-dimensional space of a level , the bifurcation level πχ, the determination of the periodic state description is possible.

Determination of the periodic description of the condition

Furthermore, a freely definable curve is selected, which is, however, in the bifurcation plane family II.

In general, a periodic description of the state can be described for each point along the curve using the following function:

xc ((tt)) == cc _nD vv (λλ) ee ^iiaυJ ^ ^Wl - ++ cc _D vv ((λλ)) ee ^" i ^ιω ω ( ^w λ) t ^L ++ yy ((λλ)) (3 ).

The following applies:

ω (λ) = Im (μ (λ)).

The factor c _p is chosen such that CpV (λ) gives the point P.

This general approach to describing a periodic state from equation (3) is generally not a solution to the differential algebraic system. This means that the following relationship applies:

f (x (t), x (t), λ) ≠ 0 (4).

In order to determine a solution and thus a periodic description of the state within the bifurcation plane family II along the curve, it is necessary that regulation (3) leads to a solution of the differential algebraic equation system.

This can be solved in such a way that an additional penalty term F (t) is taken into account, which has the following structure:

F (t) = -f (x (t), x (t), λ) (5).

The following power function P (t) results:

P (t) = x (t) ^τ f (x (t), x (t), λ) (6).

T is the time at which the technical system is described. Clearly, x can be viewed as a flow rate of a mechanical dynamic system.

An energy function E (t) can be determined from the power function P (t) by integrating the power function P (t) over a period of the respective oscillation:

E (λ) x (t) ^τ f (x (t), x (t), λ) dt

For a periodic solution of a differential algebraic

The energy function E (t) is totally balanced, since the following rule applies to this:

f (x (t), x (t), λ) = 0 (8). This applies to all times t.

In other words, this means that a balanced energy function E (t) is a property of a periodic solution of a circuit. This property can also be used to determine a point with which it is possible to estimate a good periodic state description of the circuit.

The point is determined by determining the energy function E (λ) for a point of the curve along the curve m freely definable interval steps. Since it can be shown that a zero of the real part of the energy function Re {E (λ)} on the respective evaluated

If a point on the curve gives a very good point with which a very good periodic description of the state of the circuit can be determined, a zero of the real part of the energy function Re {E (λ)} of the technical system is determined.

To determine the zero point of the real part of the energy function Re {E (λ)}, any method for one-dimensional zero point analysis, which is also referred to as a derivative-free zero point method, can be used.

It is advantageous that the curve is a semi-open, circular curve around the Hopf bifurcation point.

As a guide for the size of the curve depending on the Hopf bifurcation point and the eigenvalue μo of the Hopf

Bifurcation point is given the following dimensioning proposal, which has proven to be advantageous.

An ellipse around the Hopf bifurcation point, also as a half-open curve, whose secant along the first solution curve of the stationary solutions is approximately max. 2% of the parameter range to be examined, in which the system parameter λ varies symmetrical around the Hopf bifurcation point has proven to be advantageous. A value between 0.1 and 1 volt is suitable for the height of the ellipse.

For the zero point, i.e. for the determined point on the

The periodic state description x (t) belonging to the point is determined on the curve.

A periodic solution of the circuit is determined for the periodic state description x (t), e.g. using the procedure described in document [6].

The periodic description of the state x (t) of the circuit is the periodic solution of the circuit for the system parameter λ.

The periodic status description is used as a starting solution for the determination of further periodic solutions, starting from the starting solution, that is, the periodic status description.

Since a very good approximation for a solution on the second solution curve near the Hopf bifurcation point was determined with the starting solution, it is now possible, by using the tracking method described in [7], to perform other periodic solutions of the circuit that relate to one another the second solution curve.

This is continued iteratively until a periodic solution to a predefinable operating point of the circuit has been determined.

The method of harmonic balance can be used, for example, as a method for determining the periodic solution for a system parameter λ. The result of an iteration is therefore whether the instance of the oscillator circuit 200 is oscillating or not.

If the instance of the circuit swings, a second binary value 101 is inserted in the matrix 100 in each case in the field, which is clearly determined by the dimensions of the capacitances Cχ_, Cχ2. However, if the instance swings, a first binary value 102 is assigned to the corresponding field m of the matrix 100.

From the resulting oscillation region 103, which is limited by the respective instances that oscillate, a set of instances is selected for which the entire transient response of the quartz oscillator circuit is determined.

A method for determining the transient response of a quartz oscillator is carried out in accordance with the method described in [3].

In the following, some alternatives for the exemplary embodiment described above are shown.

It is not necessary to examine all instances of the oscillator circuit 200. Starting from a starting point 104, instances are, clearly speaking, subjected to the stability analysis in a diagonal of the 2-dimensional matrix 100, in the case of a high-dimensional matrix corresponding to a space diagonal of the hyperspace described by the high-dimensional matrix. This procedure is shown in FIG. 1 by an arrow 105 in the matrix 100. The diagonal is followed until an instance of the circuit does not start. This instance is identified in the matrix 100 by the reference symbol 106.

Starting from the first instance, which does not oscillate, a step-like procedure, the path of which is represented by an arrow 107 or 108 in the matrix 100, performed along the edge region of stable and unstable instances.

This procedure corresponds to a scanning of the edge area, so that it is not necessary to check a large partial area m of the entire matrix 100.

As described above, the dimensional act of the matrix 100 is arbitrary. Accordingly, the other components are basically arbitrary and, as described above, a wide variety of parameters can be taken into account in the circuit simulation.

In general, it should be noted with respect to the start-up area 103 that the closer the value of the determined Hopf bifurcation point 301 for the instance to the supply voltage V _Q , the more critical is the safe start-up of the oscillator circuit 200.

4 shows a computer 400 with which the method is carried out. The computer 400 has a memory 401, a processor unit 402, which is connected to the memory via a bus 403

401 is connected to. In the memory 401 is a description of the oscillator circuit 200 in a circuit description language, e.g. SPICE saved. The processor unit

402 is set up in such a way that the method steps described above for circuit simulation can be carried out. Furthermore, a screen 404 is provided for displaying the results, and a keyboard 405 and a mouse 406 for giving information to the computer 400. The following publications are cited in this document:

[1] L. 0. Chua, C. A. Desor, E. S. Kuh, Linear and Nonlinear Circuits, Mc Graw Hill, ISBN 0-07-010898-6, New York, pp. 644-687, 1987

[2] R. Neubert, An Effective Method for the Stability Analyzes of Steady States in the Simulation of Large Electronic Networks, 2nd ITG discussion session, New applications of theoretical concepts in electrical engineering, W. Mathis, P. Noll (ed.), VDE-Verlag, Berlin, ISBN 3-8007-2190-2, April 1995, pp. 41-48 [3] Qinghua Zheg, Hopf Bifurcation in Differential Algebraic Equations and Applications to Circuit Simulation, Internat. Series of Numerical Mathematics, Vol. 93, Birkhäuser Verlag Basel, ISBN 0-9176-2439-2, pp. 45-58, 1989 [4] R. Neubert, Predictor-Corrector Techniques for

Detecting Hopf Bifurcation Point, boarding school. Journal of Bifurcation and Chaos, Vol. 3, No. 5, ISSN 0218-1274, World Scientific Company, pp. 1311-1318, 1993 [5] EP 0 785 619 A2

[6] U. Feldmann et al, Algorithms for Modern Circuit Simulation -AEÜ, Vol. 46, No. 4, ISSN 0001-1096, Hirzel-Verlag, Stuttgart, pp. 274-285, 1992

[7] R. Seydel, Numerical Computation of Periodic Orbits that Bifurcate from Stationary Solutions of Ordinary Differential Equations, Technical University of Munich, Department of Mathematics, TUM-MATH-12-81-M12-250 / 1-FMA, pp. 1- 43, 1981

[8] DE 44 11 765 AI

Claims

claims 1. Method for determining an oscillation range of an electrical circuit, which has at least one oscillator and further components that are connected to the oscillator, by a computer, in which, in an iterative process, varying the wiring parameters of the other components, each for an instance of the wiring parameters the following steps are carried out: a stability analysis of the circuit is carried out for the respective instance, - If it is determined for the instance of the circuit that the instance is swinging, a first value is assigned to the instance in a matrix in which all examined instances are stored, the first value indicating that the instance is swinging, If it is determined for the instance of the circuit that the instance does not oscillate, the instance is assigned a second value in the matrix, the second value indicating that the instance does not oscillate, - in which the start-up range results from the instances to which the first value in the matrix has been assigned. 2. The method of claim 1, wherein the stability analysis is carried out according to one of the following methods: - Determination of a Hopf bifurcation point for the respective instance, - Pole zero analysis, - AC analysis (small signal analysis) using the Bode criterion or the Nyquist criterion, - transient analysis. 3. The method of claim 1 or 2, wherein the wiring parameters of the further components have at least one of the following parameters: - different temperatures to which the circuit is exposed, - different quality of the other components, - Different dimensioning values of the other building elements. 4. The method according to any one of claims 1 to 3, in which a stability analysis is carried out at the working point for at least some of the instances. 5. The method according to claim 4, wherein a determination of the transient behavior of the instance is carried out for at least some of the instances. 6.Device for determining an oscillation range of an electrical circuit which has at least one oscillator and further components which are connected to the oscillator, with a processor unit which is set up in such a way that in an iterative process with variation of wiring parameters of the further components in each case the following steps are carried out for an instance of the wiring parameters: a stability analysis of the circuit is carried out for the respective instance, - If it is determined for the instance of the circuit that the instance is swinging, a first value is assigned to the instance in a matrix in which all examined instances are stored, the first value indicating that the instance is swinging, - If it is determined for the instance of the circuit that the instance does not oscillate, a second value is assigned to the instance in the matrix, the second value indicating that the instance does not oscillate, - the oscillation range results from the instances, to which the first value in the matrix has been assigned. 7. The device according to claim 6, wherein the processor unit is set up such that the stability analysis is carried out according to one of the following methods: determination of a Hopf bifurcation point for the respective instance, - pole zero analysis, - AC analysis (small signal analysis) using the Bode criterion or the Nyquist criterion, - transient analysis. 8. Apparatus according to claim 6 or 7, in which the processor unit is set up in such a way that the wiring parameters of the further components have at least one of the following parameters: - different temperatures to which the circuit is exposed, - different quality of the other components, - Different dimensioning values of the other construction elements. 9. Device according to one of claims 6 to 8, in which the processor unit is set up in such a way that a stability analysis is carried out at the operating point for at least some of the instances. 10. The apparatus of claim 9, wherein the processor unit is set up such that a determination of the transient response of the instance is carried out for at least some of the instances.